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Additionally, the board is generated on first click guaranteeing empty space where you click.

How does he guarentee it?

Normally you'd do that by quickly reshuffling the mines if you guess wrong, although he might've gone the route of checking if it's possible to get into a guess-only state during generation and regenerating the board until no such states exist.

The source code (mines.c) is here:

https://git.tartarus.org/?p=simon/puzzles.git;a=blob;f=mines...

There is code for solving a grid using deductions in this section:

https://git.tartarus.org/?p=simon/puzzles.git;a=blob;f=mines...

And below that is the code that generates grids and checks that they are solvable without taking risks.

A similar approach is used to analyse the difficulty of Sudoku games here:

http://hodoku.sourceforge.net/en/index.php

with different names for the different types of deduction.

Thank you so much! This helps so much.

This rendition of the game is amazingly satisfying. Thanks!